On the attractors of Feigenbaum maps
A solution of the Feigenbaum functional equation is called a Feigenbaum map. We investigate the likely limit set (i.e. the maximal attractor in the sense of Milnor) of a non-unimodal Feigenbaum map, prove that it is a minimal set that attracts almost all points, and then estimate its Hausdorff dimension. Finally, for every $s\in (0,1)$, we construct a non-unimodal Feigenbaum map with a likely limit set whose Hausdorff dimension is $s$.